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IEEE/ASME TRANSACTIONS ON MECHATRONICS 1

An Avian-Inspired Passive Mechanismfor Quadrotor Perching

Courtney E. Doyle, Student Member, IEEE, Justin J. Bird, Taylor A. Isom, Jason C. Kallman, Daman F. Bareiss,David J. Dunlop, Raymond J. King, Jake J. Abbott, Member, IEEE, and Mark A. Minor, Member, IEEE

Abstract—Flying robots capable of perch-and-stare are desir-able for reconnaissance missions. Inspired by an adaptation thatenables songbirds to sleep in trees without active muscle control,the research presented herein details the design for a passive mech-anism that enables a rotorcraft to perch reminiscent of a birdperching on a tree branch. Perching is accomplished through theintegration of a compliant, underactuated gripping foot and a col-lapsing leg mechanism that converts rotorcraft weight into tendontension in order to passively actuate the foot. Analysis of mecha-nism behavior is presented, and stability tests were performed tocharacterize the ability of the system to reject disturbances. Theresults indicate that it is possible to passively perch a rotorcrafton multiple surfaces and support reasonable environmental dis-turbances. The analysis in this paper can enable passive perchingdesign optimization in vertical take-off and landing systems.

Index Terms—Bioinspired, grasp, passive actuation, perch-and-stare, tendon, underactuation.

I. INTRODUCTION

P ERCH-AND-STARE describes a maneuver in which arobot flies to a vantage point and lands to collect intel-

ligence. A robot capable of perch-and-stare, equipped withcameras and other sensors, can provide an inconspicuous re-connaissance platform. Additionally, robot perching provides apotential means for recharging the robot’s power source (e.g.,through the use of photovoltaics).

Our work aims to provide a landing mechanism that expandsthe number of surfaces upon which a rotorcraft can land. Inspiredby the perching capability of songbirds (order Passeriformes),we present a design that can perch on a variety of surfaces [seeFig. 1(a)]. Songbirds exhibit a particulary interesting adaptationthat equips them for life in the trees [1], [2]. As depicted in

Manuscript received November 1, 2011; revised April 15, 2012; acceptedJuly 8, 2012. Recommended by Guest Editor M. Sitti. This work was sup-ported in part by the University of Utah and in part by the National Sci-ence Foundation under Grant DGE-0654414. This paper was presented inpart at the 2011 IEEE/RSJ International Conference on Intelligent Robots andSystems, San Francisco, CA, September 25–30.

The authors are with the Department of Mechanical Engineering, Uni-versity of Utah, Salt Lake City, UT 84112, USA. (e-mail: [email protected]; [email protected]; [email protected]).

This paper has supplementary downloadable material available athttp://ieeexplore.ieee.org, provided by the author. The material consists of avideo, viewable with Windows Media Player, demonstrating the ability of theavian-inspired passive mechanism to: 1) support a quadrotor under external dis-turbances and 2) perch from flight using a mock-flight/control set-up. The sizeof the video is 33.7 MB. Contact [email protected] for further questionsabout this work.

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TMECH.2012.2211081

Fig. 1. Passive perching concept. (a) Quadrotor perching on a cylindricalrailing. The grip is actuated by the weight of the quadrotor. (b) Songbirds haveevolved a useful adaptation that allows for sleeping while perching. As the birdfolds its legs, the tendons on the rear side of the ankle automatically grip thetoes around the branch. This enables the relaxed leg of a sleeping bird to tightlygrip the perch without any voluntary muscle effort. Figure recreated based onan image in [3].

Fig. 1(b), songbirds have a tendon on the rear side of the anklethat automatically causes the toes to grip around a branch whenthe leg bends. This tendon enables songbirds to sleep whileperching without active control of gripping. As a bird relaxes,the weight of its body causes the legs to bend and the toes togrip; deeper relaxation leads to a tighter grip. When the birdis ready to take off, it must actively stand up to let go of theperch. This anatomy is key to the development of our passivelyactuated system; the weight of the rotorcraft is used to actuatethe gripping mechanism. When the rotorcraft lifts off, the footwill naturally release.

In addition, birds’ feet are underactuated, meaning they havemore degrees of freedom (dof) than muscles to control them,which enables the feet to passively conform to the structureon which they are attempting to perch. Underactuated grippersare a focus of study for many research groups, and designs havebeen developed that utilize passive mechanical components suchas compliant mechanisms [4]–[9] and mechanical limits [4],[6], [7], as well as clever differential transmissions [4], [6]–[11].A number of groups have developed designs that utilize four barmechanisms or gears to transmit force and move the fingers [4],[5], [10], [11]; however, more related to our study are under-actuated hands driven by tendons. One of the earliest systemswas developed by Hirose and Umetani consisting of a multilink,two-fingered mechanism driven by a pair of wires (flexor andextensor) wrapped around successively smaller pulleys [12]. Asimilar design was used at Northeastern University to developGraspar, a three-fingered hand capable of grasping a varietyof objects [13]. Other groups have employed a single tendonfor flexing while utilizing springs for a restoring force [6]–[8];

1083-4435/$31.00 © 2012 IEEE


2 IEEE/ASME TRANSACTIONS ON MECHATRONICS

the group at Universite Laval is capable of controlling a 15-dof hand with a single motor [6]. Of particular interest to usis an underactuated design of Dollar and Howe in which an 8-dof four-fingered hand is controlled using a single actuator [9].Their design uses compliant joints between stiff link segmentswith a cable secured at the distal links to transmit actuationforce, and is shown to be capable of grasping objects of varyingsize and shape. To date, a single study has investigated robotgripping inspired by the foot of a bird. Researchers at Clem-son University analyzed the feet of raptors, motivated by theirexcellent grasping ability and simple design relative to anthro-pomorphic hands [14]. They went on to design a “thumbless”grasping hand reminiscent of a raptor foot [15], but most of thejoints have independent actuation.

A number of research groups have pursued solutions to robotperching. Researchers at the University of Florida and col-leagues [16] developed a fixed-wing robot with crawling legs,designed to land on a relatively large target zone, such as thetop of a building, and then use its legs to crawl to the edge ofthe building. Researchers at Drexel University [17] equippeda miniature rotorcraft with optic-flow and ultrasonic sensors,enabling the robot to find and land on the edge of a building.Researchers at Cornell University [18] are incorporating a mor-phing structure inspired by the wings and tail of a bird duringlanding. Researchers at MIT [19] have developed a method toperform a high-speed maneuver with a fixed-wing robot, suchthat the robot pulls up into a high angle-of-attack to perch ona string via a latching hook. Researchers at the US Air ForceAcademy [20] have developed two concepts, one where the air-craft rests over an open space, suspended by four anchors, andthe second where a plane uses a sticky pad to adhere to a verticalsurface. Researchers at Ecole Polytechnique Federale de Lau-sanne [21] use impact-driven microspines to adhere to inclinedand vertical surfaces. Researchers at Stanford University [22]have used a high angle-of-attack approach to attach a fixed-wingaircraft to a vertical surface. They use a compliant, bio-inspiredleg-type mechanism as a suspension system between the aircraftand foot that uses microspines for adhesion. Other study fromthis lab [23] utilizes compliant, underactuated structures for sup-porting a wall-climbing robot. Researchers at the University ofPennsylvania [24] have used actuated, compliant microspineson a quadrotor for landing on vertical and horizontal surfaces.Each of these methods shares the need for a specific landingsurface; the ultimate goal of our avian-inspired approach is tooffer perching on the same variety of surfaces available to birds.Currently, our design performs best on horizontal objects with across section smaller than the foot, enabling an encircling grasp.

Recently, a group at Yale University attached an underac-tuated hand to the underside of a helicopter [25]. Their studyfocused on picking up objects and the effect on flight dynamics,but landing is still accomplished using traditional landing skids.

There has not been any investigation of bird-feet-inspiredgraspers for perching, other than our preliminary study [26]. Inthat work, we presented an initial prototype of a compliant legmechanism, cut from a single piece of material, that actuatedan underactuated compliant gripper. The initial prototype wasexperimentally shown to be capable of perching on cylindrical

surfaces. However, the design suffered from limited cyclic life,and its behavior deviated from the idealized model. In this paper,we present a new design with increased stability and cycliclife, more predictable behavior, and capability of perching on avariety of surfaces. It is believed that the original design is bettersuited for small-scale applications, as forces will be smaller,reducing the negative aspects, and the design presented hereinis difficult to produce at small scales. Beyond the extension ofour previous analysis to the new design, this paper provides ananalysis of foot motion and its mapping to tendon displacementand tension, as well as a stability evaluation of the system. Thecurrent design is a proof of concept, and the dimensions arenot optimized for any particular rotorcraft. In fact, the rotorcraftused herein was added after the design was complete only toillustrate the functionality of the mechanism.

II. PASSIVE LEG MECHANISM

This section presents a design iteration for the leg mechanismthat improves upon our previous work by increasing stability andcyclic life. The leg consists of a knee and ankle joint and threerigid segments: the thigh, shin, and heel. The key difference isthat the single-material compliant joints have been replaced withpin joints; this reduces fatigue, reduces out-of-plane motion,generates more idealized behavior, and enables a more exactsystem analysis. A parallelogram linkage for the shin, with pinjoints vertically aligned, enforces that the two joints deflectat the same rate and that the aircraft body keeps a constantorientation. An inelastic cable is used to actuate the attachedfoot (see Section III). The term tendon is used throughout thispaper in keeping with the bio-inspired design, but should not beconfused for an elastic material.

The design must satisfy two requirements: 1) rotorcraft cen-ter of mass (COM) must stay relatively centered over the foot;and 2) tendon path length must increase as the mechanism col-lapses. The first idea accounts for system stability during thelanding maneuver and the second idea is imperative for pas-sive actuation. Design for the first requirement is presented inSection II-A and design for the second requirement is presentedin Section II-B. Design for mechanical advantage is presentedin Section II-C.

A. Centering Rotorcraft Mass During Vertical Motion

As the rotorcraft lowers onto the perch, its COM must staycentered over the foot and the leg should not exert a momentat the foot that causes it to move out from under the body.Studying the free-body diagram presented in Fig. 2 providesdesign rules that must be followed to enforce proper motion.First, summing forces in the y-direction, and assuming the ver-tically aligned pin joints support equal forces, Fw = 1

2 Fy1a =12 Fy1b = 1

2 Fy2a = 12 Fy2b = Fp . Second, summing forces in the

x-direction, Fx1a = Fx1b = Fx2a = Fx1b . Finally, performinga moment balance on links 1 and 3 and solving for L1 andL3 : L1 = (Fx1ap)/(Fw cos φ) and L3 = (Fx2bp)/(Fp cos φ).Substituting the force balances results in the design require-ment, L1 = L3 = L. The force/moment balance does not placerequirements on L2 , but in order to keep the rotorcraft COM


DOYLE et al.: AN AVIAN-INSPIRED PASSIVE MECHANISM FOR QUADROTOR PERCHING 3

Fig. 2. Free-body diagram of the leg. Inset depicts the full leg with linksegments indicated.

over the foot L2 = 2L. A different value for L2 could be used ifthe leg is not aligned below the rotorcraft’s COM; however, thiswould impose a moment at the top of the leg, which would alterthe moment balance of the system and change the requirementson L1 and L3 .

The position of the rotorcraft mounting point, relative to thefoot, is dependent on the angular deflection of each joint [seeFig. 3(a)]. Placing the origin at the foot, the location of eachjoint and the aircraft body are determined as follows:

A = (Ax,Ay ) =(−L cos φ,L sin φ +

p

2

)

B = (Bx,By ) = (Ax + 2L cos α,Ay + 2L sin α)

C = (Cx,Cy ) =(Bx − L cos φ,By + L sin φ +

p

2

)(1)

where α = θ − φ.In order to minimize the horizontal motion of the aircraft

during collapse, a min–max optimization on |Cx | of (1) is runwith respect to φ over a desirable range of motion for eachjoint θ. For the range 0◦ ≤ θ ≤ 40◦, the optimal value of φ is16.5◦. Fig. 4(a) shows the horizontal deviation for φ = 16.5◦,L = 152.4 mm and p = 38.1 mm; the values of L and p are thedimensions used in our prototype, which were arbitrarily chosento create a mechanism roughly scaled for a quadrotor that wasable to actuate our foot. The vertical motion of the rotorcraft isshown in Fig. 4(b).

B. Vertical Motion to Tendon Pull

The tendon routing through the leg can be visualized inFig. 3(b). The change in tendon path length is dependent on twofactors: a wrapping of the tendon around each cam, and a changein length of the tangent between the two cams. By designing thetwo cams to be symmetric, the model reduces to two sets ofidentical triangles that intersect at a common point, as seen inFig. 5(a). Studying a single set of triangles [see Fig. 5(b)] thetendon path length t is determined by summing the arc length ofthe tendon in contact with the cam, tarc = 2r (3π/2 − γ), and

Fig. 3. Leg models superimposed on a SolidWorks rendering. (a) Geometricmodel. L is the length of the heel/thigh links, p is the distance between thejoints of the parallel shin links, θ is the angle between links, α is the anglebetween the shin and horizontal, and φ is the fixed angle between the heel/thighand horizontal. A and B are the pivot points located half way between thephysical pin joints of the shin links, O is the origin where the foot attaches tothe leg, and C is the point at which the aircraft attaches to the leg. The exactlocations of O and C are arbitrary, but once selected all other parameters arereferenced from their location. (b) Energy balance model. Fw is the weight ofthe rotorcraft, Fa is the tension applied to the foot, Δ is the change in heightof the rotorcraft measured from the point when the foot begins to close, δ is thechange in tendon path length just above the foot, and Kf is the effective springconstant of the foot (there is no physical spring in series with the cable, otherthan the compliant foot).

Fig. 4. Rotorcraft motion during collapse. φ = 16.5◦, L = 152.4 mm, andp = 38.1 mm. (a) Horizontal shift from center. (b) Height above the foot.

the length of the tangent line between the two cams T , as

t = 2r

(3π

2− γ

)+ T. (2)

tarc is defined assuming that the tendon wraps 3/4 of the camwhen γ = 0◦; although the tendon will actually contact slightlyless than 3/4 of the circumference, we are concerned with the



Fig. 5. Geometry of tendon path length. (a) Total length from joint to joint.(b) Detail view of half the system. θ, α, L, A, and B are as defined previously.a and b are the centers of the circular cams, c is the distance between the centerof the cams, T is the distance between the tangent points at which the tendonleaves each cam, r is the radius of each cam, q is the distance between therotation point and the center of each cam (assumed to be horizontal), and γ , γ1 ,and γ2 are defined as shown.

change in path length δ, not the actual length t, so this approxi-mation does not affect the final result.

The task now lies in determining values for γ and T . Exam-ining Triangle 1, trigonometric identities can be used to firstdetermine c and then γ1

( c

2

)2= q2 + L2 − 2qL cos(π − α) (3)

sin γ1

L=

sin(π − α)c/2

. (4)

Next, examining Triangle 2, geometric and trigonometric iden-tities can be used to determine T and γ2

r2 +(

T

2

)2

=( c

2

)2(5)

tan γ2 =T/2r

. (6)

Finally, the angle γ is known, as the sum of γ1 and γ2 . The twoparameters of interest are thus:

T = 2√

q2 + L2 − r2 + 2qL cos(θ − φ) (7)

γ = sin−1

(L sin(θ − φ)√

q2 + L2 + 2qL cos(θ − φ)

)

+ tan−1(

T

2r

). (8)

Fig. 6. Tendon path length versus vertical displacement. As the leg collapses,tendon path length increases. The total effect on tendon travel δ due to qis insignificant (< 3%) for φ = 16.5◦, L = 152.4 mm, p = 38.1 mm, andr = 31.7 mm.

A plot showing how the tendon path length changes withvertical motion is presented in Fig. 6, where the values of φ, L,and p are chosen as before and r = 31.7 mm is the value usedin our prototype, which was chosen to provide an appropriateamount of tendon travel based on our prototype foot. Plots forboth q = 6.35 mm, which is the value on our prototype, andq = 0 mm are shown. Subsequent analysis becomes difficultwith q �= 0 due to noninvertible functions, so q = 0 is used tofurther analyze the system; the error introduced in δ is minimal(< 3%), as demonstrated by Fig. 6. T and γ are simplified withq = 0, and the tendon path length t is described as follows:

t=2r

(3π

2− tan−1

(√L2 − r2

r

)+ θ − φ

)+ 2

√L2 − r2 .

(9)

C. Rotorcraft Weight to Tendon Tension

The amount of tension available to close the gripper is relatedto the weight of the rotorcraft. Performing an energy balance onthe system shown in Fig. 3(b)

Fw Δ =12Kf δ2 . (10)

Considering the leg collapsed by some nominal value Δ, col-lapsing the system by a differential change dΔ produces

Fw (Δ + dΔ) =12Kf

(δ2 + 2δdδ + dδ2) . (11)

Substituting in (10), recognizing that dδ2 can be neglected,and substituting in the locally linear relationship Fa = Kf δ,(11) can be solved for the mechanical advantage of the systemFa/Fw , which relates the weight of the rotorcraft to tendontension at the foot. Note that dCy = −dΔ and dt = dδ, so

Fa

Fw=

dΔdδ

= −dCy

dt. (12)

Thus, the mechanical advantage of the system is found by dif-ferentiating Cy with respect to t.

Cy of (1) can be expanded as

Cy (θ) = 2L sin(θ − φ) + 2L sin φ + p. (13)



Fig. 7. Parameters characterizing joint geometry. w is the width of the toe, His the height of the toe, h is the height of the joint, l is the length of the joint, ris the radius of the joint fillet, and φ is the notch angle.

But we need Cy (t), not Cy (θ), so solving (9) for θ gives thefollowing:

θ =3π

2+ Q − tan−1 Q + φ − t

2r(14)

where Q =√

L2 − r2/r. Thus, substituting (14) into (13), weobtain

Cy (t) = 2L sin(

3π

2+ Q − tan−1 Q − t

2r

)+ 2L sin φ + p.

(15)Differentiating (15) with respect to t produces the following:

dCy

dt= −L

rcos

(3π

2+ Q − tan−1 Q − t

2r

)(16)

which can be written with respect to θ as

dCy

dt= −L

rcos (θ − φ) . (17)

The mechanical advantage has a minimum value of 4.4 whenthe leg is fully open and a maximum value of 4.8 approximatelyhalf way through collapse.

III. UNDERACTUATED GRIPPING FOOT

A desirable characteristic of the bird foot is the underactuatedstructure. This allows the toes to passively conform to unknownsurface shapes. Our foot is a simplified variation on [9]. Using awaterjet, individual toes were cut from a sheet of polyurethane(McMaster-Carr Item 8716K736), using notches to create flex-ible joints. Hollow tubing was attached to the underside of eachtoe segment for tendon routing. This simple design, using asingle material, was chosen for ease of manufacturing and scal-ability. Design of the foot is presented first by characterizing thejoint in Section III-A, then analyzing motion in Section III-B.

A. Joint Characterization

Each toe joint (see Fig. 7) can be classified as a small-lengthflexural pivot and is represented by its pseudo-rigid-body modelas a pin joint with a torsion spring of stiffness K = EI/l0 , whereE is the Young’s modulus, I is the cross-sectional moment ofinertia, and l0 is the flexible segment length [27]. Because ourflexible segment does not have a uniform cross section, due to thenotch taper, validation of this model was necessary. By hangingknown weights from samples with varying parameters, we wereable to investigate the instantaneous center of rotation (ICR) and

Fig. 8. Instantaneous center of rotation (ICR) does not vary significantly as ajoint deflects. Image overlays joint at four deflection positions. The ICR, desig-nated by the white dots, is determined by drawing the perpendicular bisectorsof the line segments connecting similar points between deflections.

stiffness of each joint. It was found that the ICR of individualjoints do not vary significantly (see Fig. 8) and that stiffnessis linearly related to the geometric term wh3/l. Therefore, thepseudo-rigid-body model is valid for representing joint motion.

Combining joints in series produces a toe structure that canpassively comply to a surface. The stiffness of each joint wasdetermined by two central requirements: 1) for the largestworkspace, and thus largest range of gripping capability, it isdesirable for the joints to deflect in order from proximal to dis-tal; and 2) each joint should be able to return to some nominaldeflection with no applied tendon tension.

The first requirement can be satisfied by enforcing that K1 <K2 < . . . < Kn , as demonstrated in Fig. 9, where joint 1 is themost proximal. Notice how the gripping ability changes for eachjoint pattern. The top row shows a toe with the proposed pattern,K1 < K2 < K3 . The toe makes contact with the object startingwith the first segment, followed by the second and then third,making a successful closure. The middle row shows a toe withthe pattern K1 = K2 = K3 . For the perch shown, the toe is ableto make a closure, but each segment makes contact at roughlythe same time. For an unsymmetrical perch this toe will not beable to grip reliably. The bottom row shows a toe with the patternK1 > K2 > K3 . This toe experiences significant deflection atthe third joint first, which causes the toe to miss closure aroundthe perch.

To satisfy the second requirement, we enforce K1 > K1min,where K1min is determined by the weight of the distal portionof the toe supported by the first joint and a desired nominal de-flection. Because the first joint will experience the most weight,and each successive joint is stiffer than the previous, it followsthat each joint satisfies the second requirement so long as the



Fig. 9. Depiction of how joint stiffness patterns affect form closure. (Toprow) K1 < K2 < K3 ; (Middle row) K1 = K2 = K3 ; (Bottom Row) K1 >K2 > K3 .

Fig. 10. Joint stiffness as a function of deflection. Values are calculated usingthe mean joint deflections. Error bars show the range of K values possible withall permutations of ±σ in joint deflection, where σ is the standard deviationsof recorded joint deflections. Stiffness is nonlinearly related to deflection andincreases as the toe deflects further.

first joint does. The above constraints were used to create threeidentical toes, which are attached to the leg using an adaptationof the anisodactyl arrangement.

The stiffness component of the pseudo-rigid-body model wasinitially assumed constant, following the work of [27]. Themodel, however, was derived under the assumption that theflexible member experienced pure bending; this is not a validassumption in our toes; thus, the stiffness must be derived. Asingle toe was mounted such that the first link was horizontaland the distal links sagged under their own weight. Calibratedweights were hung from the tendon, using a pulley to convertvertical motion of the weight into horizontal tendon pull, and thedeflection of each joint was recorded. The process was repeatedthree times to analyze repeatability. The subsequent joint stiff-ness is calculated using the recursive formula presented next,and can be visualized in Fig. 10. Notice that the stiffness in-creases nonlinearly as the joints deflect through larger angles.

Fig. 11. Toe model for deflection through free space. (a) Parameter and geo-metric labeling of toe. θi is the angular displacement of link i with respect tolink i − 1. (b) Free body diagram of link i. Mi is the moment of joint i, mi

is the mass of link i, g is the gravitational constant, lc i is half the link length,where the mass is applied, Σθi is the sum of all joint angles from θ1 to θi , Ft isthe tendon tension, αi and βi are the tendon departure angles from link i, andlα and lβ are the moment arms through which the tendon forces are applied.(c) Free body diagram of link n, which is the most distal. h is the momentarm through which the tendon is attached and the remaining parameters are asdefined before.

B. Joint Motion

Utilizing the joint model, we can study a free-body diagramof the toe to predict motion and relate it to tendon displacementas well as tendon tension (see Fig. 11). With this analysis, we areneglecting the friction due to tendon movement and assumingonly tension components in the y-direction act on the interme-diate links. Furthermore, it can be shown that αi = π/2 − θi/2and βi = π/2 − θi+1/2. Finally, for each joint, Mi = Kiθi .Performing moment and force balances, if joint deflection andtendon tension are known, joint stiffness can be determined, asdepicted in Fig. 10. The recursive formula for joint stiffness is



Fig. 12. Model used to determine toe deflection to grip a cylindrical perch. His the height of the toe, Li is the length of link i, R is the radius of the perch, θi

is the deflection of joint i, and α is the angle between the contact points of linki and i − 1.

presented in (18)–(23). Alternatively, if joint stiffness and ten-don tension are known, joint deflection can be determined byrearranging the equations and iteratively stepping through therecursion until an equilibrium deflection is reached.

Kn =1θn

(Ft

(lαn sin

(θn

2

)+ h

)

+mng

(lcn cos Σθn − h

2sin Σθn

))(18)

Rxn = Ft − mng sin Σθn (19)

Ryn = Ft sin(

θn

2

)+ mng cos Σθn (20)

Ki =1θi

(Ft

(lαi sin

(θi

2

)+ lβ i sin

(θi+1

2

))

+2lci (Ryi+1 cos θi+1 − Rxi+1 sin θi+1)

+mig

(lci cos Σθi −

h

2sin Σθi

)

+ Ki+1θi+1

)(21)

Rxi = Rxi+1 cos θi+1 + Ryi+1 sin θi+1

− mig sin Σθi (22)

Ryi = Ft

(sin

(θi

2

)+ sin

(θi+1

2

))+ mig cos Σθi

+ Ryi+1 cos θi+1 − Rxi+1 sin θi+1 (23)

We now present an analysis to determine the joint deflectionsrequired to grip a circular cross section of a particular radius R,which can be used to determine the necessary displacement ofthe actuating tendon. Studying Fig. 12, two similar triangles are

Fig. 13. Model used to determine tendon pull required to deflect a joint. (a) Toein undeflected shape. (b) Toe in deflected shape. j0 is the size of the undeflectedjoint notch where the tendon is routed, j is the size of the deflected joint notch,c is the distance from the tendon to the ICR, and θ is the joint deflection.

formed with equal angles θi = α. From the larger triangle,

cos α =R + H

R + H + b(24)

tan α =a + Li−1/2

R + H. (25)

From the smaller triangle,

cos θi =Li

2a(26)

tan θi =2b

Li. (27)

Equating (24) with (26) and (25) with (27) produces the systemof equations that can be solved for b, which is substituted into(27) and solved for θi

θi = tan−1

(2Li

(L2

i + Li−1Li

)(R + H)

4(R + H)2 − L2i

). (28)

The amount that the tendon must be pulled to create thesedeflections is now calculated by studying the joint geometryshown in Fig. 13. First, the initial values ψ and s must bedetermined through geometry from Fig. 13(a)

ψ = 2 tan−1(

j0

2c

)(29)

s =

√j20

4+ c2 . (30)

Next, the new gap length is calculated through geometry fromFig. 13(b)

j = 2s sin(

ψ − θ

2

). (31)

Finally, the required tendon pull δ can be calculated as thedifference between the two notch lengths, and summed overeach joint

δ =n∑

i=1

(j0i − ji) (32)

where j0i is the original notch length and ji is the deflectednotch length of joint i.



Fig. 14. Differential system applied to tendons, where F1 and F2 are thetendon tensions in individual toes and Fa is the tendon tension applied by theleg.

IV. COMPONENT INTEGRATION

For maximum grasping adaptability, it is desirable that eachtoe be able to move semi-independently. A pulley block is uti-lized to create differential actuation of each toe (see Fig. 14).The tendon routed from the leg is tied to one side of the pulleymount and the front toe is tied to the opposite side of the mount.The two back toes are connected by a single tendon, routedaround the pulley. The tendon in each toe will displace at equiv-alent rates through open space, providing symmetric closure. Ifmotion in one of the back toes is constrained, the pulley systemwill allow the remaining toes to move δ and 2δ for the front andback toe, respectively. Furthermore, through open space, thissetup creates an equal force distribution among each of the toes,such that F1 ≈ F2 ≈ Fa/3. This is an approximate relationshipbecause the tendon does not necessarily depart the pulley in adirection parallel to Fa ; deviation will cause slight variationsin tension. Once motion in one back toe is constrained, the twoback toes will still experience equivalent tension, but the tensionin the tendon of the back toes will increase at twice the rate ofthe front toe due to the change in displacement rates.

The tendon material is a fused superline (10 lb Berkley Fire-Line Fused Crystal), which has high strength with minimalstretch. A soft Buna-N foam (McMaster-Carr, Item # 93745K21)and coarse sandpaper (60 grit emery cloth) was applied to thesurface of each toe segment to provide greater friction at thegrip. Additionally, two mechanical pin-type stops were addedto each cam to restrain the motion of the leg when freely dan-gling beneath the rotorcraft.

Two leg mechanisms were attached to a Gaui 330X QuadFlyer. The quadrotor weighs 388 g and has a payload of 700 g,which must include a battery. After attaching our mechanisms,we witnessed an undesirable amount of independent actuationbetween the two legs, which caused instability in perching. Tomitigate this, we added two stabilizers connecting the legs atthe heel and thigh, which caused the legs to move more de-pendently. Because of compliance in the joints, the legs canstill collapse to slightly different heights, providing the abilityto perch on surfaces of different cross sections. The completedtwo-leg mechanism weighs 478 g, which leaves 222 g for bat-teries and future additions such as cameras or GPS systems. Forreference, the 2200 mAh lithium polymer battery we are usingweighs 145 g, which means there is 77 g remaining in the pay-load; this value will likely need to be increased, which wouldrequire reducing the weight of the leg and foot. The completesystem can be visualized in Fig. 15.

V. EXPERIMENTAL STABILITY EVALUATION

The functional quality of the landing gear was studied throughfour experiments. First, we studied the ability of the landing gear

Fig. 15. Mechanism in initial (Left) and final (Right) perching states. Thepulley is used to indicate the tendon motion.

to support a quadrotor while perching on a variety of surfaces.Second, we studied the ability of the landing gear to support aquadrotor under angular perturbations from vertical. Third, westudied the ability of the landing gear to support the quadro-tor under lateral disturbances. For the first three experiments,the system was manually placed on the perches. A fourth testexplored perching using a mock flight setup.

A. Versatile Perching Capability

To understand the versatility of the landing gear, the systemwas perched on a variety of commonly found surfaces. The sys-tem is able to perch on many types of surfaces, but performs beston surfaces that allow the toes to wrap around the perch. Thecylindrical railing in Fig. 1 is similar to the PVC tubing used totest the mechanism during development. Similarly, the system isable to perch on a tree branch, Fig. 16(a), which is roughly cylin-drical but not homogeneous in geometry and texture. Fig. 16(b)shows the system perching on a rectangular railing, where thefoot is just large enough to grip around the front of the surface;qualitatively, this perch is remarkably stable, and the sharp cor-ners seem to act to lock the toes in place. On more oddly shapedsurfaces, the system can succeed in perching; however, itsstability is less predictable. For example, Fig. 16(c) and (d)shows the system perching on exposed plumbing; the perchshown is at equilibrium, but slight angular deviations of thequadrotor resulted in unstable perches. Notice that the systemis not only able to stabilize on perches with uniform foot stance[see Fig. 16(c)], but also on perches with nonuniform foot stance[see Fig. 16(d)]. Fig. 16(e) shows the system on a rock withnonuniform topography.

Additionally, we are interested in how the system lands onflat surfaces. As shown in Fig. 16(f), the legs tilt forward and thesystem comes to a resting position on the feet and the knee joints.Although this orientation may not be ideal, it is repeatable andstable. The ability of a rotorcraft to take off from this positionwill need to be investigated before determining if this is anacceptable landing position.

B. Stability Under Angular Perturbations

It is unreasonable to expect a robotic rotorcraft to be ableto land on the perch perfectly vertically. When perched at anoff-center angle, the full rotorcraft weight is not available toactuate the gripper, and a portion acts to pull the system out of



Fig. 16. Successful perches on common objects. (a) Tree branch. (b) Rect-angular railing. (c) Plumbing, with similar foot stances. (d) Plumbing, withasymmetrical foot stances. (e) Ridge of rock. (f) Flat ground.

equilibrium. As such, we explored the range of angles at whichthe system is stable. The experimental setup consisted of a perchthat could freely rotate, with an Arduino Mega microcontrollerand a GMS high-torque servo motor to control rotation of theperch (see Fig. 17). With the servo initialized at 0◦, the landingmechanism and rotorcraft were centered on the perch; the servothen stepped through rotation in increments of 1◦ and held for30 s. The point at which the landing mechanism released wasrecorded. Twenty readings were averaged to quantify variance.This method was performed for both positive and negative an-gles on painted PVC perches of 33- and 49-mm diameters,where a positive angle is defined as one that tilts the front ofthe rotorcraft toward the ground. The results are summarized inTable I. At large angles (� 10◦), the servo motor was not ableto completely overcome the moment imposed on the perch andoften sat at a slightly larger angle than that being commanded;thus, the data reported here are a conservative estimate. It is alsoimportant to note that the values reported here are sensitive tothe tendon tensioning.

There are two important trends to notice from the data. First,the system has a higher tolerance to angular perturbations onthe smaller perch; this is because the quadrotor sits closer to theperch, so the COM acts at a smaller moment arm than on thelarger perch. As such, it may be beneficial to determine charac-teristic minimal perch size for a given application, then design

Fig. 17. Perturbation test setup. (Left) Angular perturbation test setup. (Right)Additional components for lateral perturbation test.

TABLE IANGULAR STABILITY LIMITS

the leg so that the aircraft sits low for that size perch. Second,the system has a higher tolerance to angular perturbations inthe negative direction; this may be due to the structure of theleg. For instance, when the leg collapses, the shin links are atan angle such that the knee is lower than the ankle; this meansthat as the aircraft tilts forward (positive angles) the pitch of theshin is exaggerated and the COM of the leg produces a highermoment. However, when the aircraft tilts backward (negativeangles), the shin links approach horizontal and the COM of thelegs produces a lower moment.

As an initial investigation of grip materials, we repeated thetest on a 42- mm diameter commercial fence toprail and includedthree additional grip materials reported to have good surfacefriction characteristics: a natural rubber (McMaster-Carr Item93625K248), a silicone rubber (McMaster-Carr Item 5781T48),and a polyvinyl foam mesh (McMaster-Carr Item 85695K1).The new materials were also tested on the 49-mm PVC perch.The results are summarized in Table I. Data for the naturalrubber are not included in the table because it performed worsethan the original sandpaper material. From the data, it appearsthat the polyvinyl mesh is a better material for gripping ability.Further tests for durability should be performed before makinga final selection.



TABLE IILATERAL FORCE LIMITS

C. Stability Under Lateral Disturbances

Once the system has made a stable perch, it will likely experi-ence environmental disturbances such as wind. In this scenario,the full rotorcraft weight is actuating the gripper, but the lateralforce acts to pull the system out of equilibrium. Thus, we de-signed an experiment to test the amount of horizontal force thesystem can withstand. The setup from the angular perturbationtest was reused, and a pulley was added so that a horizontal forcecan be applied by hanging weights on a cable (see Fig. 17). Thequadrotor was set at angles of 0◦ and 1/2 the magnitude of themaximum angular perturbation in the positive and negative di-rections from Table I for sandpaper on the painted PVC perches.Weight was applied to a cable that was secured to the bottomplate of the quadrotor and held for 30 s. The point at whichthe feet slipped off the perch was recorded. Ten readings wereaveraged to quantify variance. This method was performed onperches of 33- and 49-mm diameters for positive and negativeforces, where a positive force is one that acts to move the ro-torcraft forward. The results are summarized in Table II, withequivalent values for the acting moment disturbance at the foot,calculated as the product of the force and the distance fromthe center of the perch at which the force is applied (137 and180 mm for the 33- and 49-mm perches, respectively).

When perched away from vertical, the most obvious thing tonotice is that there is an asymmetry between the disturbancesthat can be supported in the negative and positive directions.This is as expected. Take, for example, the 33-mm perch at −7◦:here, a negative force pulls the system in the same direction asgravity and into a larger angle, but a positive force pulls thesystem against gravity and into a smaller angle.

Although a point force is not the same as a wind gust, thesedata give an idea of the amount of disturbance that can be sup-ported as it is seen as a moment at the foot. An initial attemptwas made to correlate lateral force to an equivalent wind speed.We used the Treadport Adaptive Wind Tunnel (TPAWT) devel-oped at the University of Utah [28]. The TPAWT directs windflow to augment the experience of a virtual reality participant.With the TPAWT, we were not able to consistently achieve windspeeds that caused our perching mechanism to fail, so a rigor-ous analysis of the capabilities cannot currently be provided.Reliably, an environment with average wind speeds of the or-der of 5 m/s and gusts up to 6.5 m/s could be created; in this

Fig. 18. Mock flight test setup. (a) Marionette strings attached at each motor,maintained parallel to the motor axes. (b) Experimenter guided the quadrotorusing a marionette with 1.7 m strings. Strings are highlighted in blue for clarity.

setting, the quadrotor on the 33-mm painted PVC perch wasagitated by the disturbance, but did not release the grip. Whenfailure was induced, gust values varying from 8 to 12 m/s wererecorded, where the wind vector was clearly a significant factorfor stability.

D. Mock Perching From Flight

At this time, we do not have autonomous flight control algo-rithms, so it is not possible to present perching reliability fromflight. However, in order to approximate system performancefrom flight, we set up a rig similar to a marionette. Four 1.7 mstrings, one per motor, were attached to a cross such that, whenhanging, the strings pulled in a direction parallel to the propelleraxis of rotation. As long as the string stays closely aligned withthis axis, any applied force represents an equivalent thrust fromthe propeller.

Two scenarios were run, each with ten attempts, and the suc-cess rate was recorded. A successful perch was defined as onewhere the quadrotor remained stable on the perch after the guidestrings were slack. A total of six trials were run, alternatingwhich scenario was performed first, to determine an averageand standard deviation; a 15-min break was taken between eachtrial in order to reduce human learning and fatigue. Scenario Arepresents a flight control capable of accurately centering therotorcraft over the perch, but has no control of the final descent.We lifted the quadrotor off the perch and rested in a hover-likeposition, while the toes were allowed to bump the perch and sta-bilize the COM over the perch. The quadrotor was then quicklydropped, meant to represent a shutoff of the motors. ScenarioB represents a flight control capable of both centering over theperch and controlling the decent. For the setup, we slowly low-ered the rotorcraft from above, allowing adjustments providedthe string remained parallel with the rotor rotation axes. The testsetup can be visualized in Fig. 18.

Scenario A had a success rate of 73 ± 9% and Scenario B hada success rate of 98 ± 4%. These numbers tell us that if a controlalgorithm is developed that can closely center the rotorcraft overthe perch, the rotorcraft should find a stable perch most of the



time. If the algorithm is also capable of controlling the decent,the success rate should increase significantly. These results arepromising for future development of autonomous flight.

VI. DISCUSSION AND FUTURE WORK

Results from the stability experiments show that the current,unoptimized design is capable of passively supporting moderateexternal disturbances. The stability range can be improved byincreasing the friction at the grip. Friction can be increasedwith a better selection of contact material on each toe; an initialstudy was presented in Section V-B, but a more rigorous studyof materials may provide even better results.

Additionally, friction can be increased by increasing the nor-mal force at each contact point, which directly correlates to themechanical advantage of the system. Future iterations will usean optimized leg design, to provide the best mechanical advan-tage for our quadrotor. The equations presented in Section IIcan be used to optimize the leg dimensions for a given foot, bal-ancing required tendon travel with mechanical advantage. Theequations in Section III can be used to optimize foot dimensionsfor a desired application, balancing required toe deflection withtendon pull and joint stiffness.

A concern for grip strength is line-stretch over time. Initially,we used a monofilament fishing line for our tendon material,which experienced significant stretch within the first cycle. Wethen upgraded to the fused superline, which has minimal stretch.More significant than tendon stretch is slippage at the tensioningscrews; improving this connection is a goal for the next proto-type. Fortunately, moderate slack in the tendon does not renderthe mechanism useless. The slack is analogous to backlash ingeared systems, requiring the quadrotor to lower a small amountbefore engaging the gripper, shifting the system on the mechan-ical advantage curve. As long as the slack is not excessive, thesystem can still maintain sufficient grasp.

Other topics for future consideration are material selection,altering toe design, studying flight dynamics, and integrating aflight controller. The current leg and foot materials were cho-sen out of convenience; the current mechanism is within thepayload of the rotorcraft, however lighter materials will allowfor additional items such as surveying cameras and sensors to beadded to the quadrotor. By altering the toe design, both lengthand number of segments, it is possible that better grips canbe achieved. Now that the concept has been shown feasible,the ability to fly with the mechanism attached must be studied.This ultimately will result in the development of a controller forautonomous flight and perching. Current work in autonomousquadrotor flight suggests that a controller can be developed forstable flight. The mock flight conditions presented in Section V-D lead us to believe that a controller can be developed to controlthe landing maneuver.

VII. CONCLUSION

The prototype presented in this paper demonstrates that robotperching on a variety of surfaces can be achieved through theintegration of a passive actuating mechanism with an underac-tuated gripper. Stability tests demonstrated the range of distur-

bances that can be supported. Although this current prototypeperforms relatively well, improvements can be made in futuredesign iterations. One topic of interest is studying the effects ofaltering toe length and the number of segments; it is possible thatbetter grips on a wider variety of surfaces can be achieved byaltering these characteristics. Also, the current prototype dimen-sions were chosen somewhat arbitrarily so that the mechanismwas scaled approximately to the size of a quadrotor and achievedat least the minimum tendon pull and tension necessary to closethe foot; using the governing equations presented herein, moreoptimal dimensions can be selected to reduce weight and im-prove performance. Finally, the effect of the landing gear onflight dynamics, and methods to mitigate this effect, remainsthe most significant open question.

ACKNOWLEDGMENT

The authors would like to thank C. Johnson and J. Simpsonfor their contributions to the design of the leg and acknowledgethe support of T. Slowik in the Department of Mechanical En-gineering. Additionally, they would also like to thank Dr. R.Meyers at Weber State University for fruitful discussions aboutbird anatomy and function.

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Courtney E. Doyle (S’10) received the B.S. degreesin mechanical and electrical engineering from theUniversity of Michigan, Ann Arbor, in 2007, and theM.S. degree in mechanical engineering from the Uni-versity of Utah, Salt Lake City, in 2011, with workfocusing on the bio-inspired grasping mechanisms.She was awarded an IGERT Traineeship from NSFfor Biocentric Robotics at the University of Utah,where she is currently working the Ph.D. degree inmechanical engineering, studying human–robot in-teraction related to emotions and expression.

Justin J. Bird received the B.S. degree in mechanicalengineering from the University of Utah, Salt LakeCity, in 2011.

He is currently working in the Kennecott CopperDivision of Rio Tinto.

Taylor A. Isom received the B.S. degree in mechan-ical engineering from the University of Utah, SaltLake City, in 2011.

He is currently working as an automation engineerat Bard Access Systems.

Jason C. Kallman received the B.S. degree in me-chanical engineering from the University of Utah,Salt Lake City, in 2011.

He is currently working as a 3D modeler atK’nowbe Works, LLC.

Daman F. Bareiss received the B.S. degree in me-chanical engineering in 2011 from Oklahoma StateUniversity, Stillwater. He was awarded an ARCSFoundation scholarship and an IGERT Traineeshipfrom the NSF for Biocentric Robotics at the Univer-sity of Utah, Salt Lake City, UT, where he is currentlyworking toward the Ph.D. degree in mechanical en-gineering, investigating the interactions between hu-mans and highly maneuverable, human-ridden mo-bile robots.

David J. Dunlop received the B.S. and M.S. de-grees in mechanical engineering from the Univer-sity of Utah, Salt Lake City, in 2010. He performedresearch in the field of precision machine design.He was awarded an IGERT Traineeship from theNSF for Biocentric Robotics at the University ofUtah, where he is currently working toward thePh.D. degree in mechanical engineering, studyingquadrupedal robotic gait.

Raymond J. King received the B.S. and M.S. degreesin engineering science and mechanics from VirginiaTech, Blacksburg, in 2009 and 2010, respectively. Heis currently working toward the Ph.D. degree in me-chanical engineering in the University of Utah, SaltLake City, where his work consists of modeling thetendon system of the human hand.

He was the recipient of the IGERT Traineeshipfrom NSF for Biocentric Robotics, University ofUtah.

Jake J. Abbott (M’06) received the B.S. degree fromUtah State University, Logan, in 1999, the M.S. de-gree from the University of Utah, Salt Lake City, in2001, and the Ph.D. degree from The Johns HopkinsUniversity, Baltimore, MD, in 2005, all in mechani-cal engineering.

In 2005, he became a Postdoctoral Research Asso-ciate at ETH Zurich, Switzerland. In 2008, he becamean Assistant Professor in the Department of Mechan-ical Engineering, University of Utah, where he is cur-rently the Head of the Telerobotics Laboratory.

Dr. Abbott is the recipient of the NSF Faculty Early Career DevelopmentAward, and the 2010 ICRA Best Manipulation Paper Award.

Mark A. Minor (M’00) received the B.S. degreein mechanical engineering from the University ofMichigan, Ann Arbor, in 1993, and the M.S. andPh.D. degrees in mechanical engineering from Michi-gan State University, East Lansing, in 1996 and 2000,respectively.

He is currently an Associate Professor in the De-partment of Mechanical Engineering, University ofUtah, Salt Lake City, where he has been a facultymember since 2000. His research interests focus ondesign and control of robotic systems including mo-

bile robots, rolling robots, climbing robots, flying robots, autonomous groundvehicles, and virtual reality systems.

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